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Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered…

This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a…

Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…

In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…

In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…

This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223--242] for target distributions with a noncompact support. The…

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans through graph partitioning. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest…

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian…

Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of complex statistical distributions, and while bypassing the cumbersome requirement of a specific analytical expression for the target, this stochastic exploration…

In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…

We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies…

We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…

This work introduces a class of rejection-free Markov chain Monte Carlo (MCMC) samplers, named the Bouncy Hybrid Sampler, which unifies several existing methods from the literature. Examples include the Bouncy Particle Sampler of Peters and…

We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…